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中国物理学会期刊

基于量子机器学习的压缩量子模拟

Compressed Quantum Simulation via Quantum Machine Learning

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  • 量子模拟利用可控的量子系统来模拟一个难以用经典计算机处理的复杂多体量子系统,以应对随多体系统规模指数增长的计算复杂度。本文研究了一种基于量子机器学习的压缩量子模拟方案,通过利用参数化量子线路构建量子自编码器,学习高维希尔伯特空间中量子绝热演化的低维等效表示,并在低维空间中高保真地重构绝热演化过程以实现压缩量子模拟。本文以 9 量子比特二维横场伊辛模型的量子相变检测问题为例,使用 2 量子比特系统对其进行压缩量子模拟,制备基态并测量磁涨落和能量等物理量。结果表明,该方案能在低维希尔伯特空间中高精度复现量子相变行为,所得基态能量的相对误差不超过 2.1%。本研究为在资源有限的量子设备上模拟复杂物理过程提供了新的思路,推动了量子模拟与机器学习的交叉融合。

     

    Numerically simulating quantum many-body systems is known to be a difficult computational problem, especially for large systems. This difficulty may be overcome through quantum simulation, which uses some controllable quantum system to study another less controllable or accessible quantum system. Compressed quantum simulation can reduce experimental resource requirements, and can provide more resource-efficient implementations of quantum simulations. In this work, we propose a quantum machine learning based compressed quantum simulation scheme. A quantum autoencoder is trained on a small set of representative instantaneous ground states. After training, the autoencoder can map the adiabatic path onto a compressed subspace and yields low-dimensional representations of the Hamiltonians and relevant observables. These effective operators are then used to reconstruct the full adiabatic evolution and evaluate physical quantities entirely within the compressed Hilbert space. As a demonstration, we employ this compression scheme to simulate the quantum phase transition of a 9-qubit 2D Ising model on a 2-qubit quantum processor. During training, the loss converged to 0.008, corresponding to a mean fidelity of 0.992 between the reference-subsystem state and its target state. Then we demonstrate that the adiabatic evolution can be realized on a smaller quantum system and the magnetic-fluctuation, whose cusps indicate quantum phase transitions can be measured in the experiment. In this effective evolution, we reproduce the finite-size critical response of the original system near g\approx0.35, with a root-mean-square error of 0.046 and a coefficient of determination R^2=0.962 relative to the exact calculations. Moreover, the maximum relative error in the ground-state energy is 2.05\%, while the fidelity between the reconstructed state and the original 9-qubit ground state remains more than 0.96, confirming that our compressed simulation closely reproduces the original adiabatic evolution. For improved quantum-resource efficiency, the effective two-qubit Hamiltonian contains only nine nontrivial Pauli terms, compared with 27 terms in the original representation, thereby reducing the circuit depth required for digital quantum simulation. These results show that quantum phase transitions in systems larger than the available quantum processor can be investigated experimentally using current quantum technology.

     

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